Triangulation complexity and systolic volume of hyperbolic manifolds

Lizhi Chen

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arXiv · 2109.09194

Triangulation complexity and systolic volume of hyperbolic manifolds

Lizhi Chen

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Abstract

Let $M$ be a closed $n$-manifold with nonzero simplicial volume. A central result in systolic geometry from Gromov is that systolic volume of $M$ is related to its simplicial volume. In this short note, we show that systolic volume of hyperbolic manifolds is related to triangulation complexity. The proof is based on J{\o}rgensen and Thurston's theorem of hyperbolic volume.

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Lizhi Chen. 2021-09-19. Triangulation complexity and systolic volume of hyperbolic manifolds. https://arxiv.org/abs/2109.09194

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